2094
J. Phys. Chem. 1996, 100, 2094-2099
Validation of Hybrid Density Functional/Hartree-Fock Approaches for the Study of Homogeneous Catalysis Vincenzo Barone* Dipartimento di Chimica, UniVersita` di Napoli “Federico II”, Via Mezzocannone 4, I-80134 Napoli, Italy
Carlo Adamo Dipartimento di Chimica, UniVersita` della Basilicata, Via Nazario Sauro 85, I-85100 Potenza, Italy ReceiVed: August 22, 1995; In Final Form: October 23, 1995X
The potentialities of a hybrid density functional/Hartree-Fock approach in the study of homogeneous catalysis have been investigated by a comprehensive study of binary adducts of copper atom characterized by strong (Cu2, CuH, CuCH3) or weak (CuCO, CuNO, CuO2, CuC2H2) metal-ligand interactions. The results confirm that this approach describes with good accuracy several properties of transition metal complexes, giving in particular binding energies close to the best available post-Hartree-Fock and experimental results. Besides the reasonable computation times, the possibility of avoiding high angular momentum basis functions, and the negligible basis set superposition error, the strength of hybrid approaches is their remarkably constant accuracy for closed- and open-shell systems and for strong covalent or weak donor-acceptor interactions. Furthermore, the ease of interpretation of single-determinant methods is retained. This allows the use of powerful energy decomposition tools for gaining further insight into the origin of different bonding patterns.
1. Introduction The theoretical analysis of transition metal complexes has been an area of great interest to theoretical chemistry for a very long time and for several reasons. From one side there is the challenge of predicting accurate molecular properties (geometries, dissociation energies, etc.) in systems that, due to the large number of electrons, are particularly difficult to describe. From another side, there is the interest of understanding the role of metal-ligand interactions in catalytic processes in which these complexes are often involved. In the case of heterogeneous catalysis, a fundamental understanding has been developed by studying the reactivity of metal clusters as a function of cluster size.1 On the other hand, homogeneous catalysis occurs in solution and normally involves monomulclear transition metal complexes. In analogy with the cluster approach for heterogeneous catalysis, an attractive approach for understanding homogeneous reactions is to start by studying the reactivity of isolated transition metal atoms and then examine the effects of added ligands. From an experimental point of view, several cationic species have been characterized using mass spectrometric techniques, whereas the investigation of neutral species is less developed due to several experimental problems. From a theoretical point of view, such model systems are ideally suited for calculations, but the evaluation of reliable molecular properties is still far from being a routine task. At the present state of the art, the most reliable methods to study the properties of transition metal compounds are probably the different variants of the coupled cluster (CC) model2 or of the multireference configuration interaction, starting from a complete active space (CAS) SCF wave function.3 However, these methods are very expensive already for small model compounds and absolutely out of question for large systems. In this scenario, the development and validation of less conventional theoretical tools is mandatory. The messa-a-punto of accurate X
Abstract published in AdVance ACS Abstracts, January 1, 1996.
0022-3654/96/20100-2094$12.00/0
functionals, including gradient corrections, makes the density functional (DF) approach the most useful nonempirical alternative to conventional post-Hartree-Fock (HF) methods.4 Several recent studies5-7 show that DF approaches based on the generalized gradient approximations (GGA) can model with remarkable accuracy the properties of heavy transition metals, whereas some problems, especially concerning binding energies, have been found for complexes involving first-row transition metals.8-12 On this line, we and others11-14 have recently found that significantly improved results can be obtained by the socalled self-consistent hybrid (SCH) approaches. Rooted in the adiabatic connection formula, SCH methods include some Hartree-Fock (HF) exchange to capture the characteristics of systems with low electron-electron couplings, poorly described by current density functionals. The above-mentioned studies document that this improvement allows to obtain reliable general trends as a function of the nature of the metal. However, a nearly constant accuracy for ligands with different characteristics (e.g., basicity, degree of unsaturation, etc.) is a mandatory prerequisite for any reliable investigation of homogeneous catalysts. This task is not trivial since it is well-known that, already for organic molecules, the reliability of conventional methods of intermediate degrees of sophistication decreases when going from saturated to unsaturated compounds or from closed-shell species.15 We thought interesting to investigate whether SCH approaches are sufficiently reliable also in this connection. In this first study we have selected a transition metal, i.e. copper, without nearly degenerate electronic states and for which several experimental16-34 and conventional quantum-mechanical35-46 studies are available. Furthermore, the binding energies (De) of the studied complexes cover a wide range, going from strong covalent bonds (De > 50 kcal/mol) to weak noncovalent interactions (De < 15 kcal/mol). Taking also into account that both closed- and open-shell systems have been considered and that different coordination modes are possible in some cases, we think that this study provides a particularly severe challenge for any quantum-mechanical approach. © 1996 American Chemical Society
Homogeneous Catalysis 2. Computational Details The calculations reported here are based on the unrestricted Kohn-Sham (UKS) approach47 to the density functional theory as implemented in the Gaussian 92/DFT package.48,49 In SCH methods50,51 the exchange-correlation energy (EXC) is represented by the following general equation UEG EXC ) EXC + (1 - a0)(EXHF - EXUEG) + aX∆EX + ac∆EC (1)
where EXUEG is the density functional for the exchange energy is the corresponding of the uniform electron gas,52 EUEG C correlation contribution,53 EXHF is the Hartree-Fock exchange, and the ∆E terms are the GGA contributions to exchange and correlation. The B3LYP variant is obtained using the Becke gradient correction to exchange,54 the Lee-Yang-Parr (LYP) correlation functional,55 the semiempirical coefficients of eq 1 determined by Becke51 from a best fitting of the heats of formation of a standard set of molecules (a0 ) 0.80, aX ) 0.72, and aC ) 0.81), and the approximation ∆EC ≈ ELYP C . EVWN C In order to avoid any numerical noise, we have used for numerical integration a quite large grid consisting of 75 radial shells and 302 angular points per radial shell for each atom. The TZ2P′ orbital basis set used in all the computations has been purposely optimized by B3LYP atomic computations and is explicitly given and validated in ref 12 for Cu and in refs 58-60 for second-row atoms. Geometries of all the energy extrema have been fully optimized by gradient methods and their nature (minima or firstorder saddle point) characterized by diagonalizing the matrix of second derivatives obtained analytically. This has also allowed to compute harmonic vibrational frequencies and the contribution of zero-point energies (ZPE) to binding energies. Finally, the characteristics of metal-ligand interactions have been analyzed by a powerful energy partitioning technique based on the so-called natural bond orbitals (NBO),65 which allows to quantitatively describe the electronic state of the partners in a complex and to isolate donation and back-donation contributions to metal-ligand interactions. 3. Results and Discussion Before discussing in detail the various compounds, we wish to make some general comment about conventional post-HF and DFT methods. In the former case, accurate results for transition metals can be obtained by coupled pair functionals (e.g., MCPF62), different implementations of the CC ansatz (QCISD(T),63 CCSD(T),64,65 BD(T),66 etc.), or multireference approaches (e.g., CIPSI,67 MRDCI,68 CASPT269). The requirements of these methods in terms of basis sets are very stringent (e.g., f and g functions must be used), and for multireference approaches, the selection of the active space is particularly delicate.70,71 Since very few computations can be considered converged in terms of the basis set and/or the reference space, these approaches usually overestimate metal-ligand bond lengths and underestimate bond strengths. The errors of DEbased approaches are exactly in the opposite direction since inadequacies of the current functionals lead to an overestimation of correlation energy. A. CuH and Cu2. The B3LYP molecular parameters of CuH are reported in Table 1. The MH bond length is 1.474 Å, very close to the experimental estimate of 1.463 Å. Previous MCPF computations37 give a value of 1.494 Å, whereas the CASPT2 approach leads practically to the experimental value
J. Phys. Chem., Vol. 100, No. 6, 1996 2095 TABLE 1: Bond Lengths (R in Å), Vibrational Frequencies (ω in cm-1), and Dissociation Energies (De and D0 in kcal/mol) Computed for CuH, CuH+, and Cu2 at the B3LYP/TZ2P′ Level Are Compared with the Available Experimental Data; In Parentheses Are Reported the Results Including Relativistic Corrections Estimated in Ref 72 (CuH) and in Ref 77 (Cu2) system
method
R
ω
De
D0a
CuH(1Σ+)
B3LYP expb B3LYP
1873 (1949) 1941 262 (276) 267
61.8 (64.6)
Cu2(1Σg)
1.474 (1.449) 1.463 2.282 (2.242) 2.219
59.2 (62.0) 60.0 ( 1.4 42.7 (44.3) 48.0
expc
43.0 (44.6)
a
Including ZPE corrections. b References 22 and 23. c References 20 and 21.
(1.466 Å).36 Both results have been obtained with very large basis sets, which include up to g functions. The longer bond length, at the B3LYP level, influences also the Cu-H stretching frequence, which is 60 cm-1 lower than the very close CASPT2 (1936 cm-1) and experimental (1941 cm-1)21 values. On the other hand, the B3LYP model outperforms the CASPT2 method in the prediction of the dissociation energy (59.3 vs 64.1 kcal/ mol, to be compared to an experimental estimate of 60.0 ( 1.4 kcal/mol20). Our computations completely neglect relativity. Relativistic effects on the structure and properties of CuH have been recently estimated.72 It has been found that, while spinorbit effects are negligible, Darwin and mass-velocity operators cause a sizable contraction of s orbitals, which, in turn, lead to a slightly shorter and stronger bond. Adding the best estimates of these effects to B3LYP results (see Table 1) does not modify general trends but leads to results more in line with those obtained at the same level for hydrides of main group atoms. The copper dimer is perhaps the best known and most studied of the transition metal dimers. Accurate estimates of its binding energy have been available since the pioneering work of Drowart and Honig.73 The commonly accepted value is that of Hilpert (45.66 ( 0.92 kcal/mol),74 whereas the accepted values for the bond length and the vibrational frequency are 2.220 Å and 266 cm-1, respectively. The most accurate theoretical results (bond length of 2.215 Å, an harmonic vibrational frequency of 277 cm-1, and a dissociation energy of 47.7 kcal/mol) have been recently obtained by the CASPT2 method, using a very large ANO basis set and including relativistic corrections.36 The results obtained by Bauschlicher and co-workers,38 employing the MCPF approach and a smaller basis set, are somewhat less satisfactory: 2.267 Å and 40.2 kcal/mol for the bond distance and the dissociation energy, respectively. We have found, at the B3LYP/TZ2P′ level, a slightly longer bond length, 2.282 Å, a dissociation energy of 43.0 kcal/mol, and a stretching frequency of 262 cm-1. We have also verified basis set saturation effects adding a f function (ζf ) 0.75175) on copper. The optimized bond length does not change, and the binding energy increases by only 0.1 kcal/mol. This confirms the comparatively negligible role of high angular momentum functions in DF methods. Also in this case, estimates of relativistic effects are available76 and have been included in Table 1. Note that these corrections improve the agreement with experiment for all the Cu2 properties. On the other hand, all the computations performed by conventional DF methods strongly overestimate the binding energy and tend to give a too short bond length.77 B. Two Benchmark Systems: CuCH3 and CuCO. We have selected CuCH3 and CuCO as benchmark systems for strong and weak metal-ligand interactions, respectively.
2096 J. Phys. Chem., Vol. 100, No. 6, 1996
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TABLE 2: Geometrical Parameters (Å, deg) and Dissociation Energies Computed by Different Methods for CuCH3 Using the TZ2P′ Basis Set molecule 1
CuCH3( A1)
CH3(2A′′2)
method
Cu-C
C-H
HCH
D0a
LSD BP BLYP B3LYP expb LSD BP BLYP B3LYP expc
1.853 1.902 1.923 1.921
1.099 1.098 1.095 1.089
111.2 111.0 111.3 111.3
71.3 56.5 53.3 48.7 53.3
1.090 1.087 1.085 1.079 1.078
120.0 120.0 120.0 120.0 120.0
a ZPE corrections have been computed in any case using the B3LYP/ TZ2P′ harmonic frequencies given in Table 3 and BSSE (0.5 kcal/ mol). b Reference 24. c Reference 60.
TABLE 3: Comparison between Computed (B3LYP/TZ′′P′) and Experimental Vibrational Frequencies for CuCH3 and Free CH3 molecule
method
CH
CuCH
Cu-C
CH
HCH
tilt
CuCH3(1A1)
B3LYP expa B3LYP expb
3035 2880 3112 3077
1118 1196
532 350
3132 2929 3288 3161
1445 1336 1411 1383
669 424 543 603
CH3(2A′′2) a
Figure 1. Comparison between the Cu-C bond lengths obtained by different methods for CuCO using the basis set of ref 57. Only B3LYP′ computations have been performed with the TZ2P′ basis set.
Reference 25. b Reference 60.
In Table 2 are reported the B3LYP results for the coppermethyl complex. Extensive post-HF computations have been carried out very recently for this molecule. It has been found40 that the QCISD(T) approach strongly underestimates the Cu-C bond dissociation energy, while a more accurate result has been obtained at the CCSD(T) level. These computations can be used to validate the B3LYP approach. For instance, the dissociation energy is 49.7 kcal/mol at the CCSD(T) level,42 while our result is 50.6 kcal/mol. Previous MCPF computations41 give 48.4 kcal/ mol, whereas the experimental estimate is 53.2 kcal/mol. There is also a nice agreement for geometrical parameters: at the CCSD(T) level the Cu-C distance is 1.921 Å, the C-H bond length is 1.096, and the HCH angle is 110.0°, while the corresponding B3LYP values are 1.921 Å, 1.089 Å, and 111.3°. This trend is also confirmed by the analysis of the harmonic frequencies, which are very close to the CCSD(T) values42 and in good agreement with experiments.24,25 In fact, the mean deviation is 177 and 162 cm-1 at the CCSD(T) and B3LYP level, respectively. Note that a better agreement between computed and experimental frequencies is obtained reversing the experimental assignment of the C-H symmetric and antisymmetric stretches. This is consistent with previous CCSD(T) and HF studies.42 A comparison of the performances of different functionals and basis sets is offered in Table 3. The significant improvement afforded by partial inclusion of HF exchange (cf. BLYP and B3LYP results) and the effectiveness of the TZ2P′ basis set are well evidenced. Although metal carbonyls are usually very stable, this is not the case for 1B metal atoms (Cu, Ag, and Au) in view of the extra stability of the completed nd10 configuration of these atoms. In particular, in C∞V symmetry the 2Σ+ state of the CuCO complex correlates with the 2S(3d104s1) ground state of atomic copper and the closed-shell 1Σ+ ground state of CO. Due to repulsion between the singly occupied 4s copper orbital and the highest occupied molecular orbital (HOMO) of CO, a localized lone pair on the carbon atom, this state of the complex is expected to be only weakly bonded by dipole-induced dipole interactions. Bending could at the same time reduce Cu-CO
Figure 2. Comparison between the Cu-CO dissociation energies obtained by different methods using the basis set of ref 57. Only B3LYP′ computations have been performed with the TZ2P′ basis set. Zero-point energy is always taken into account, but only the circles connected by the broken line give values corrected for BSSE. The shadowed region includes the experimental error bar.
repulsion and also allow 4s to 2π* donation, which is not possible for the linear molecule. As a consequence, the bent structure could correspond to the absolute energy minimum. The Cu-C bond bond lengths and Cu-CO dissociation energies obtained by different methods are summarized in Figures 1 and 2, whereas the B3LYP/TZ2P′ results are given in full in Table 4. All the DF methods agree in forecasting a bent equilibrium structure with a substantial barrier (≈4 kcal/mol) to linearity. It is quite apparent that the B3LYP functional gives the most satisfactory dissociation energies, thus suggesting that also for weak interactions partial inclusion of Hartree-Fock exchange significantly improves the performances of current functionals. Since variational evaluation of small binding energies can be seriously affected by the basis set superposition error (BSSE), the counterpoise method of Boys and Bernardi78 was used to correct the Cu-CO dissociation energy. Correcting the B3LYP binding energy (7.8 kcal/mol) for BSSE (0.5 kcal/mol) and zeropoint energy differences (0.7 kcal/mol) yields a value of 6.6 kcal/mol, which is in remarkable agreement with the experimental estimate of 6 ( 1 kcal/mol.28 The BSSE is less than 20% of the corresponding values obtained in recent post-HF and UKS studies (Figure 2) and well below the value of 1 kcal/ mol, which characterizes “chemically accurate” basis sets. C. CuO2 and CuNO. The structure and energetics of neutral CuO2 are well documented experimentally.17-19,78,80 In particular, Mitchell has determined that the bond dissociation energy is 15 ( 5 kcal/mol,17 while EPR experiments18,19 have been interpreted in terms of an end-on coordination (see Figure 3). On the other hand, MCPF and CCSD[T] computations43
Homogeneous Catalysis
J. Phys. Chem., Vol. 100, No. 6, 1996 2097
TABLE 4: Bond Lengths (Å), Angles (deg), Harmonic VIbrational Frequencies (cm-1), and Dissociation Energies (kcal/mol) Computed for CuCO, CuO2, CuNO, and CuON Complexes at the B3LYP/TZ2P′ Level (See Figure 1 for Definition of Geometrical Parameters) system
state
Ra
r
R
µa
1.142
139.84
0.656
1.286
116.57
0.097 (0.109) 3.869
1.366
70.00
1.193 1.173 1.204 1.168
129.47 119.00 126.88 126.53
CuCO
2
A′
1.968
free CO
1Σ+
CuOO
2A′′
1.126 (1.128) 1.915
free O2
2A 2 3Σ g
free O2-
2Π g
CuNO
3A′′ 1A′
CuON
3
A′
1A′
free NO
2Π
1.966 1.210 (1.208) 1.348 (1.35) 1.889 1.939 2.000 2.108 1.147 (1.151)
Erel
Deb 7.8
0.0
13.2
5.415 0.000 (0.000)
9.0
4.2
3.000 1.490 2.526 1.087 0.140 (0.160)
0.0 2.2 13.8 26.2
16.1 13.9 2.3 unbound
D0c
ω1a
ω2
ω3
7.1 (6 ( 1)
2041
337
225
439
214
453
173i
427 476 298 382
219 281 169 163
12.9 (15 ( 5) 4.2
15.7 13.2 2.2
2210 (2170) 1175 (1123) 1119 1612 (1580) 1163 (1090) 1602 1681 1389 1644 1956 (1904)
a Experimental values in parentheses, from ref 15, except CuCO dissociation energy,28 CuO2 dissociation energy,17 and vibrational frequency79 and O2- bond length and vibrational frequency.80 b Dissociation energy. c Dissociation energy including ZPE corrections.
Figure 3. Schematic drawing and labeling of geometrical parameters for Cu complexes having two possible equilibrium structures.
indicate that the C2V side-on (2A2 state) and the Cs end-on (2A′′ state) complexes are energetically very close to each other, with the stability order being very sensitive to the computational method. More recent CCSD(T) computations44 using the effective core potentials indicate that the C2V structure is more stable than the Cs one by about 1 kcal/mol, but the computational procedure is probably biased by the use of nonoptimal basis sets and effective potentials.72 Our results (Table 4) indicate that the end-on coordination is favored. The 2A2 state resulting from the side-on coordination is 9.0 kcal/mol higher in energy and actually corresponds to a first-order saddle point, with one imaginary frequency (173i cm-1) for the b2 bending mode. From a chemical point of view, this result is not surprising since, in principle, in the end-on structure two 3dπ and a 4s orbitals may interact with the π system of the O2 molecule, while in the sideon structure the 4s orbital cannot participate in the metal-ligand interaction. The NBO analysis allows a more detailed description of metal-ligand interactions. In particular, the copper atom in the end-on structure has a 3d9.874s0.59 electronic configuration and bears a charge of 0.530 |e-|, suggesting that in this structure the metal-ligand interaction has a partial covalent character, which arises from the interaction of the Cu 4s orbital with a sp hybrid orbital of the O2 moiety. The 3d orbitals are almost
fully filled and, being higher in energy than the π* orbital of the O2 moiety, are not involved in the bond. A corresponding NBO analysis shows that the Cu-O2 interaction in the side-on structure is essentially ionic (Cu+-O2-). In fact, the copper atom has a NBO charge of 0.857 |e-| and a 3d9.944s0.13 configuration. This picture is confirmed by the analysis of geometrical features. In fact, the O-O distance in the Cs structure is shorter than in the C2V complex (1.286 vs 1.366 Å), where it is very similar to that computed for the free O2- species (1.348 Å). The harmonic frequencies for the OO stretching follow the same trend, being 1175 and 1119 cm-1 for the 2A′′ and the 2A2 state, respectively, and 1612 and 1163 cm-1 for free O2 and O2-. On these grounds we suspect that the excessive stability of the more ionic side-on form obtained by all the post-HF methods can be traced back to their underestimation of the ionization potential of copper (7.16 eV from the most accurate computations vs an experimental value of 7.72 eV). On the other hand, the B3LYP approach overestimates the Cu ionization potential (8.03 eV), thus possibly favoring the less ionic end-on form. As regards the metal-oxygen distance, the B3LYP values are always shorter than those obtained by post-HF methods. For instance, in the side-on complexes, this bond length is 2.081 Å at the CCSD(T) level, 1.966 Å at the B3LYP level, and 1.989 Å at the MCPF level. The dissociation energy of the 2A′′ electronic state of CuO2 has been estimated as 13.2 kcal/mol, a value which is close to the experimental finding (15 ( 5 kcal/mol).17 As expected, the 2A state is only weakly bonded, the dissociation energy being 2 4.4 kcal/mol. The situation is even more involved for the complex with the nitric oxide (see Figure 3 and Table 4). Schwarz and coworkers19 have presented some evidence for the existence of the neutral CuNO species in the gas phase. They suggested that the observed species could correspond either to a single side-on complex or to the different end-on complexes (CuNO and CuON) engaged in a very fast interconversion. Using a valence-only basis set with the effective potentials of ref 81, HF and CISD approaches favor a 3A′′ state corresponding to an end-on Cu-NO coordination, whereas the 1A′ state for the same coordination becomes more stable at the CCSD(T) level.44 Our results indicate that the ground state is a triplet (3A′′), with the singlet only 2.2 kcal/mol higher in energy. Besides the order of the electronic states, there is a good agreement between B3LYP and post-HF geometries. For instance, the metal-
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TABLE 5: Geometrical Parameters (Å and deg) and Binding Energies (kcal/mol) for the Two Different Structures of CuC2H2 Cs symm C2V symm free C2H2 a
state
Cu-C
C-C
C-H1
C-H2
∠CuCC
∠H1CC
∠H2CC
Dea
D0b
2A′
2.002 2.489
1.243 1.203 1.197
1.067 1.063 1.062
1.078 1.063 1.062
113.5
157.8 174.3 180.0
138.9 174.3 180.0
3.0 0.4
2.5 0.4
2
A2 1Σ g
Dissociation energy. b Dissociation energy including ZPE corrections.
TABLE 6: Vibrational Frequencies (cm-1) for the Two Different Structures of CuC2H2 and for the Free C2H2 Molecule 2A′
2A
state
2
free C2H2•
state
sym
assignt
freq
sym
assignt
freq
sym
assignt
freq
1a′ 2a′ 3a′ 4a′ 5a′ 6a′ 7a′ 1a′′ 2a′′
C2H2 str C1H1 str CC str CH bend CCu str C2H2 bend CCu bend CH wag CH wag + CCu str
3391 3233 1772 786 495 314 170 759 579
1a1 2a1 3a1 4a1 1b2 2b2 3b2 1b1 1a2
CH str CC str CH bend CCu str CH str CH bend CCu bend CH wag CH wag + CCu str
3493 2030 766 60 3397 618 127i 757 630
1σg 2σg 1πg 1σu 1πu
CH str CC str CH wag CH str CH bend
3509 2067 655 3407 757
nitrogen bond length in the 3A′′ state is 1.889 Å at the B3LYP level and 1.911 Å at the CCSD level. A slightly longer distance (1.939 Å) is found in the singlet state (1A′). The binding energy computed at the B3LYP level indicates a rather strong bond between copper and nitric oxide (16.1 kcal/mol), which weakens in the singlet state (4.2 kcal/mol). The geometry of the nitric oxide is sensibly modified by the interaction with the metal atom. In fact, the N-O bond length goes from 1.147 Å in the free molecule to 1.173 Å in the complex (3A′′ state), in agreement with the classical interpretation of metal-ligand bonding based on donation and backdonation interactions. The ground electronic state of the CuON complex is a triplet state, about 14 kcal/mol higher in energy than the 3A′′ state of CuNO, the singlet state being further 12.4 kcal/mol less stable. The B3LYP computations indicate a Cu-O bond length of 2.000 Å, slightly longer than the Cu-O distance in the CuO2 complex, thus suggesting some interaction between the 3dπ orbital of the copper atom and the π* molecular orbital of NO. A relatively large N-O distance further supports this argument. At variance from the CuNO isomer, the CuON interaction is very weak, the dissociation energy being only 2.3 kcal/mol. As already found at the CCSD(T) level, no minimum corresponding to a side-on coordination could be located. D. CuC2H2. As in the case of the CuO2 complex, two energy minima are, in principle, possible for CuC2H2 (see Figure 3). In this case EPR experiments30,31 seem to be compatible only with the C2V side-on structure, whereas previous DF studies,46 carried out with a standard GGA model, suggest that an end-on Cs structure is more stable. The results obtained in the present study for the two different structures of CuC2H2 are summarized in Tables 5 and 6. Due to the repulsion between the singly occupied 4s copper orbital and the highest occupied molecular orbital (HOMO) of C2H2, a bonding CC π orbital, the complex is expected to be at most weakly bonded. Bending could at the same time reduce Cu-C2H2 repulsion and also allow 4s to 2π* donation, which is not possible for the C2V molecule. As a consequence, the Cs structure could correspond to the absolute energy minimum. This is confirmed by the results of Table 5. The B3LYP method agrees in forecasting a bent equilibrium structure with a nonnegligible barrier (2.6 kcal/ mol) to reach the C2V transition state. The binding energy of the Cs structure, corrected for the ZPE differences (0.5 kcal/ mol), is 2.5 kcal/mol. Even if this value is lower than the experimental estimate (6 ( 1 kcal/mol),27 the B3LYP results are close to standard GGA data, obtained with the same basis set.46
As regards geometrical parameters, the B3LYP values are slightly different from those obtained by conventional DF methods.46 In particular, the Cu-C distance in the Cs structure (2.002 Å) is longer than that obtained at the BLYP level (1.971 Å) employing the same basis set, whereas the CC distance of the vinyl moiety is shorter (1.243 vs 1.259 Å, at BLYP and B3LYP levels, respectively). Since no refined post-HF results are available, a definite conclusion on the quality of these results is still lacking. As mentioned before, the B3LYP method indicates that the C2V structure is actually the transition state for interconversion between two equivalent Cs structures with a small imaginary frequency (126i cm-1). However the low-energy difference computed between Cs and C2V structures of CuC2H2 in the present study suggests that the equilibrium between the two structures can be influenced by small intrinsic and environmental effects. The more so as the dipole moment of the vinylic form is much lower than that of the π complex (0.5 vs 3 D). 4. Conclusion We have investigated the potentialities of the B3LYP hybrid method as a general purpose tool for the study of homogeneous catalysis. Our results confirm that the tendency to overbinding of conventional DF methods is strongly reduced by the inclusion of some HF exchange, leading to results competitive with postHartree-Fock approaches. Basis set saturation is reached at levels compatible with the study of quite large systems, and the basis set superposition error is under control. When even greater accuracy is sought, geometries optimized at the B3LYP level can be profitably used for single-point computations by the most sophisticated many-body methods, and B3LYP harmonic frequencies provide reliable estimates of non-potential energy effects in determining kinetic and thermodynamic properties. Finally, the B3LYP approach allows a straightforward extension of energy partitioning techniques developed for the HF method to a model effectively including correlation effects. References and Notes (1) Metal-Ligand Interactions: From Atoms, to Clusters, to Surfaces, NATO-ASI; Salahub, D. R., Russo, N., Eds.; Kluver Academic: Dordrecht, 1992. (2) Bartlett, R. J. J. Chem. Phys. 1989, 93, 1697. (3) Raghavachari, K.; Trucks, G. W.; Pople, J. A.; Head-Gordon, M. Chem. Phys. Lett. 1989, 157, 479. (4) Ziegler, T. Chem. ReV. 1991, 91, 651. (5) Jonas, V.; Thiel, W. J. Chem. Phys. 1995, 102, 8474.
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